"Life is good for only two things, discovering mathematics and teaching mathematics"--Siméon Poissonbeen
Recently my district had in-service days for each middle school grade level focusing on the new CCSS (Common Core State Standards). I have already been applying some of the CCSS practices in my classroom the last few years, but this in-service really brought up some interesting ways to do problem-based learning.
One thing I've started incorporating in my classroom this year is a "Parking Lot Question". It's really just an Exit Ticket on a post-it note that they "park" in the parking lot on the board. After all their answers are in, I take the post-its down and stick them to a sheet of paper with the question and date written at the top of the page. Then, I put the sheet of paper in a sheet protector and put it in the Formative Assessment notebook for that class (each class has its own color for organization).
For now, the parking lot is just a 5x6 grid I drew on board, but the lines keep getting erased, so I'll probably make a permanent one on butcher paper soon. I've been using some more challenging questions and my questions are creating some incredible questions and discovery.
Recently, we have been studying the rules of exponents. I love having my students write out (a^5)(a^6) as (a*a*a*a*a)(a*a*a*a*a*a) so that they have a reason to want to find a way to multiply monomials that is shorter. My amazing students have discovered the rules multiplying and dividing powers with the same base, powers of powers, and powers of products all by using this discovery method! And they're owning it, which is my favorite.
Here is one of my favorite "Parking Lot Questions" here recently:
About half of my students answered this question incorrectly on their post-it. However, as I was listening to them discuss it as class ended, I got really excited to discuss this question more! So, today, as soon as we had gone over Warm-Ups, I put this question back on the board. Unsurprisingly, when they answered the question a second time, they all got it right... some of them changed their minds, based on the discussion they had with their peers! I love when they discover these things on their own, even more than I could possibly love just showing it to them.
So, I see more "Parking Lot Questions" in our future, and lots more discussion and discovery!